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## 'Red Balloons, Blue Balloons' printed from http://nrich.maths.org/

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Katie and Will have some balloons, some are red and some are blue.

First, Katie blew up a red one. After her first puff her balloon had a circumference of $24$ cm.

Her second puff added $\frac{1}{2}$ as much again to that.

Her third puff increased it by $\frac{1}{3}$.

Her fourth puff increased it by $\frac{1}{4}$ and her fifth puff by $\frac{1}{5}$.

Her sixth puff increased it by $\frac{1}{6}$ and at the beginning of her seventh puff it went

Next, Will blew up a blue balloon. After his first puff his balloon had a circumference of $14$ cm.

And, just like Katie's, his second puff added $\frac{1}{2}$ as much again to that and his third puff increased it by $\frac{1}{3}$.

His fourth puff increased it by $\frac{1}{4}$ and so on.

His balloon burst at exactly the same size as Katie's at the beginning of a puff.

How many puffs had Will done before his balloon burst?